1 25 Points Let X Xn Be Iid Normal 0 1 Define 1 X 0 0 X 0 Let Y P Y 1 A Find The Maximum Likel 1 (214.14 KiB) Viewed 30 times
1. (25 points) Let X₁,..., Xn be iid Normal (0, 1). Define 1 X₂ > 0 0 X ≤0 Let y = P(Y₁ = 1). (a) Find the maximum likelihood estimate of y. (b) Find an approximate 90% confidence interval for . (Hint: Use the delta method to get the standard error of the MLE.) (c) Define = (1/n) Σ, Y₁. Show that is a consistent estimator of y. (d) Compute the asymptotic relative efficiency of to. (Hint: The answer should be a function of 0.)
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of y. (b) Find an approximate 90% confidence interval for . (Hint: Use the delta method to get the standard error of the MLE.) (c) Define = (1/n) Σ, Y₁. Show that is a consistent estimator of y. (d) Compute the asymptotic relative efficiency of to. (Hint: The answer should be a function of 0.)